# Arbitrage-free neural-SDE market models

arXiv: https://arxiv.org/abs/2105.11053 · HTML: https://mlsanity.com/paper/2105.11053/

## Key facts

- Cited by 19 papers in the map (data through 14 Oct 2026).
- Builds on 3 of its 96 references that are in the map.
- First posted on arXiv 24 May 2021.

## Builds on (most cited first, 3 of 3)

- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [Robust pricing and hedging via neural SDEs](https://mlsanity.com/paper/2007.04154/) (2020)
- [Improving the Flexibility and Robustness of Model-Based Derivative-Free Optimization Solvers](https://mlsanity.com/paper/1804.00154/) (2018)

## Built on by (most cited first, 19 of 19)

- [Designing Universal Causal Deep Learning Models: The Geometric (Hyper)Transformer](https://mlsanity.com/paper/2201.13094/) (2022)
- [Global universal approximation of functional input maps on weighted spaces](https://mlsanity.com/paper/2306.03303/) (2023)
- [Multi-Asset Spot and Option Market Simulation](https://mlsanity.com/paper/2112.06823/) (2021)
- [Arbitrage-Free Implied Volatility Surface Generation with Variational Autoencoders](https://mlsanity.com/paper/2108.04941/) (2021)
- [FuNVol: A Multi-Asset Implied Volatility Market Simulator using Functional Principal Components and Neural SDEs](https://mlsanity.com/paper/2303.00859/) (2023)
- [Continuous-time stochastic gradient descent for optimizing over the stationary distribution of stochastic differential equations](https://mlsanity.com/paper/2202.06637/) (2022)
- [Universal randomised signatures for generative time series modelling](https://mlsanity.com/paper/2406.10214/) (2024)
- [Estimating risks of option books using neural-SDE market models](https://mlsanity.com/paper/2202.07148/) (2022)
- [Risk-Neutral Market Simulation](https://mlsanity.com/paper/2202.13996/) (2022)
- [Hedging option books using neural-SDE market models](https://mlsanity.com/paper/2205.15991/) (2022)
- [Causal Responsibility Attribution for Human-AI Collaboration](https://mlsanity.com/paper/2411.03275/) (2024)
- [Universal approximation property of neural stochastic differential equations](https://mlsanity.com/paper/2503.16696/) (2025)
- [DYSANOS Generative Dynamic Smooth Arbitrage-free Non-parametric Option Surfaces](https://mlsanity.com/paper/2608.12587/) (2026)
- [Conditional Deep Levy Models for Exotic Derivatives: History-Aware Path Generation and P-Q Payoff Diagnostics](https://mlsanity.com/paper/2509.13374/) (2025)
- [A Risk-Neutral Neural Operator for Arbitrage-Free SPX-VIX Term Structures](https://mlsanity.com/paper/2511.06451/) (2025)
- [Arbitrage-Free Bond and Yield Curve Forecasting with Neural Filters under HJM Constraints](https://mlsanity.com/paper/2511.17892/) (2025)
- [NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes](https://mlsanity.com/paper/2607.14361/) (2026)
- [Neural Kolmogorov Equations: Parallelizable Learning of Stochastic Dynamics under General Noise](https://mlsanity.com/paper/2607.19173/) (2026)
- [Structured Neural SDEs for Functional Calibration](https://mlsanity.com/paper/2609.34831/) (2026)

## Abstract (arXiv)

Modelling joint dynamics of liquid vanilla options is crucial for arbitrage-free pricing of illiquid derivatives and managing risks of option trade books. This paper develops a nonparametric model for the European options book respecting underlying financial constraints and while being practically implementable. We derive a state space for prices which are free from static (or model-independent) arbitrage and study the inference problem where a model is learnt from discrete time series data of stock and option prices. We use neural networks as function approximators for the drift and diffusion of the modelled SDE system, and impose constraints on the neural nets such that no-arbitrage conditions are preserved. In particular, we give methods to calibrate textitneural SDE models which are guaranteed to satisfy a set of linear inequalities. We validate our approach with numerical experiments using data generated from a Heston stochastic local volatility model.